Question

The point collinear with $(4,2,0)$ and $(6,4,6)$ among the following is

• A. $(0,4,6)$
• B. $(8,6,8)$
• C. $(1,-4,-6)$
• D. None of these
  

Answer 1

The correct option is D None of these

Cartesian form of a line passing through $(x_1,y_1,z_1)$ and $(x_2,y_2,z_2)$ is:

$\frac{x-x_1}{x_2-x_1}=\frac{y-y_1}{y_2-y_1}=\frac{z-z_1}{z_2-z_1}=\lambda$

Cartesian form of the line passing through (4,2,0) and (6,4,6) is:

$\frac{x-4}{6-4}=\frac{y-2}{4-2}=\frac{z-0}{6-0}=\lambda$

$\frac{x-4}{2}=\frac{y-2}{2}=\frac{z-0}{6}=\lambda$

Therefore general point on the line is $(2\lambda +4,2\lambda +2,6\lambda )$

Now if we compare this coordinate with given options,we get different values of $\lambda$.

that means none of the points given in options lie on the line(Non-Colinear).

Therefore, (D) option is correct.